Chernet Tuge Deressa

Malaria is a vector‐borne infectious disease primarily found in tropical and subtropical regions, where its transmission is driven by the bite of Anopheles mosquitoes. To explore the spread of malaria between two interconnected patches with varying degrees of endemicity, we developed and examined a reaction–diffusion model that incorporates the combined effects of temperature variability, malaria relapse, human diffusion, and behavioral change through awareness campaigns. We established the non‐negativity and boundedness of solutions. Next‐generation matrix techniques were employed to calculate the basic reproduction number. The stability analysis indicated that the malaria‐free equilibrium is locally and globally asymptotically stable when , but becomes unstable when . Reported case data on malaria in Ilu Ababor and Gambella, Ethiopia, from 2018 to 2025 were used to validate the model. Our findings reveal that human mobility significantly influences the geographical spread of malaria, while temperature variability notably affects mosquito biting and mortality rates. Additionally, relapse can sustain malaria transmission within the community. However, behavioral changes such as draining standing water, improving sanitation, and promoting awareness of malaria prevention can significantly reduce disease transmission and improve public health outcomes. The novelty is that, in contrast to previous models that consider only one or two factors, our model uniquely integrates temperature variability, human movement, disease relapse, and behavioral change within a single reaction–diffusion framework, validated using reported malaria case data from Ethiopia.

We develop an age‐structured malaria transmission model coupling human demographic structure with temperature‐ and humidity‐dependent mosquito life‐history parameters across all aquatic and adult vector stages, calibrated from field data collected at TIDRC, Jimma University, Ethiopia. Well‐posedness of the resulting system, which involves a dynamic rather than demographically fixed total human population, is established via integrated semigroup theory on a nondensely defined operator domain. The next‐generation operator yields in closed form as an explicit function of both climate variables, peaking at T ≈ 25.9°C, H ≈ 63.5% and exceeding unity for T ∈ [22, 31]°C regardless of humidity. Bifurcation analysis of the age‐structured PDE system produces exact closed‐form bifurcation coefficients C ₁ and C ₂ ; backward bifurcation, with its associated bistability and elimination threshold below unity, requires disease‐induced mortality to substantially exceed natural human mortality. Sensitivity analysis identifies mosquito egg deposition and adult mortality as the dominant drivers of . An optimal control problem with five intervention strategies is analyzed via the Pontryagin maximum principle; simulated interventions show indoor residual spraying can achieve elimination alone at moderate coverage, while insecticide‐treated nets are the most cost‐effective single measure. These results clarify how climate and vector demography jointly shape malaria risk and provide a rigorous mathematical foundation for age‐targeted control prioritization.

The interplay between drug‐sensitive and drug‐resistant malaria parasites within a host is a complex phenomenon that significantly impacts antimalarial treatment effectiveness and the evolution of resistance. This study analyzes the dynamical behavior of a within‐host malaria model incorporating maturation delay , immune activation delay , and competitive interactions between drug‐sensitive and drug‐resistant infected red blood cells. Using the next‐generation matrix method, we compute the basic reproduction number . The qualitative analysis reveals that the disease‐free equilibrium is asymptotically stable for any delay whenever and loses stability when . Conditions for uniform persistence of both strains are established under the Hale–Waltman framework, showing that coexistence occurs when each strain can invade the other’s boundary equilibrium. A Hopf bifurcation analysis with respect to the immune delay yields a first Lyapunov coefficient μ ₂ ≈ −0.2223, confirming a supercritical transition to stable limit cycles, providing a mechanistic hypothesis for chronic oscillatory infections. Sobol sensitivity analysis identifies sensitive‐strain drug efficacy ( ϵ _s ) and resistant‐strain death rate ( δ _{y r} ) as the most influential parameters, suggesting that combined therapy targeting both strains may be more effective than monotherapy for maintaining . However, these treatment‐related findings are model‐derived hypotheses requiring clinical validation. Numerical simulations verify the theoretical stability and sensitivity results.

Malaria is one of the most prevalent diseases spread by mosquitoes in tropical and subtropical areas. In this study, we present an age‐structured mathematical model for the within‐host dynamics of Plasmodium falciparum malaria, employing a dual age‐structured partial differential equation (PDE) incorporating chronological age, a for uninfected red blood cells (RBCs) and infected RBCs by their infection age, s . We provide a thorough mathematical analysis, such as well‐posedness, equilibrium points, basic reproduction number R ₀ , and critical delay. The disease‐free equilibrium (DFE) is locally asymptotically stable for any delay τ ≥ 0 whenever R ₀ < 1. Conversely, when R ₀ > 1, the DFE loses stability. Furthermore, the system entered a Hopf interval as τ passed through its critical value τ _c , leading to oscillations and limit cycles around the endemic equilibrium point (EEP). Moreover, we conducted an uncertainty and sensitivity analysis using Monte Carlo methods and Sobol sensitivity analysis, and we found that high uncertainty in R ₀ , given the current knowledge of parameter values, indicates high heterogeneity. Even with the substantial uncertainty reflected in the wide 95% CI, only about 15.7% of simulations produced R ₀ < 1. The results of sensitivity indicates that the age‐dependent transmission rate β _max , merozoite production rate ( α ), maximum production rate of RBCs from bone marrows π ₀ , and merozoite mortality rate μ _M are the most influential factor, taking a share of 38%, 32.7%, 26.9%, and 5% respectively. These implies that parasite replication rate (burst size) α , age dependent transmission rate β _max , and merozoite mortality rate μ _M are critical control points. Numerical simulations done by Python supports our theoretical results.

Malaria is a vector‐borne infectious disease, particularly found in tropical and subtropical regions, where its transmission is driven by the bite of Anopheles mosquitoes. To explore the malaria transmission dynamics between two patches with varying degrees of endemicity, we developed and analyzed a two‐patch Atangana‐Baleanu fractional‐order malaria model that incorporates patch‐specific optimal controls: treated mosquito nets, antimalaria drugs, and insecticide. We established nonnegativity and bounded solutions, confirming the model’s mathematical and epidemiological well‐posedness. The next‐generation matrix technique was employed to calculate the basic reproduction number. The stability analysis indicated that the malaria‐free equilibrium is locally and globally asymptotically stable when , otherwise unstable when . Actual data on the prevalence of malaria in Ilu Ababor and Gambella, Ethiopia, from 2018 to 2025 were used to validate the model. Numerical simulations indicate that human mobility significantly influences the geographical spread of malaria, while temperature variability notably affects mosquito biting and mortality rates. Furthermore, as fractional orders decrease from one, the spread of the endemic slows. Hence, by applying optimal control, we examined the effectiveness of patch‐specific, time‐dependent interventions. Results demonstrate that the combined implementation of treated mosquito nets, antimalaria drugs, and insecticide spraying significantly reduces malaria prevalence in both patches, underscoring the importance of integrated, localized intervention strategies. The main novelty lies in the fusion of fractional‐order dynamics, spatial heterogeneity (two patches and temperature variability), real‐data validation, and patch‐specific optimal controls, which collectively provide a more realistic and policy‐relevant framework than traditional malaria models that focus on a single homogeneous population.

Malaria remains a major global health threat, with the World Health Organization estimating approximately 282 million cases and 610,000 deaths in 2024. To improve the design of vaccination campaigns, we developed an age‐structured partial differential equation (PDE) model for malaria transmission that incorporates the imperfect nature of available vaccines. We performed calibration of the PDE‐based transmission model using age‐stratified epidemiological data from the Ilu Aba Bor Zone, Oromia, Ethiopia. This process involved discretizing the continuous age‐structured PDEs into a system of ordinary differential equations (ODEs) structured by age cohorts, enabling the estimation of locally relevant transmission parameters from routine surveillance data. We then formulated and solved an optimal control problem where the vaccination rate is a control function, ζ ( t , a ), dependent on both time t and age a , with the objective of minimizing the total economic burden of disease and vaccination costs. Using Pontryagin′s maximum principle, we derive the optimality system and characterize the time–age‐dependent vaccination strategy. Numerical simulations, parameterized with the data‐informed estimates, demonstrate that the optimal strategy dynamically prioritizes young children (ages 0–4) for sustained vaccination while strategically timing efforts for other key groups, a policy proven to be significantly more cost‐effective than a uniform approach. Furthermore, our analysis quantifies the price of vaccine imperfection, showing how waning immunity substantially increases the cost and effort required for disease control. By integrating rigorous mathematical modeling with local epidemiological data, this work provides a robust, evidence‐based foundation for designing targeted, resource‐efficient malaria vaccination programs adapted to the demographic and transmission characteristics of endemic regions.

Malaria remains a major vector‐borne infectious disease, particularly in tropical and subtropical places, where Anopheles mosquito bites are the primary means of transmission. Human mobility plays a crucial role in influencing the geographical distribution of malaria, whereas temperature variations significantly affect mosquito biting behavior and mortality rates. To control malaria transmission across two patches with varying degrees of endemicity, we proposed and analyzed a two‐patch compartmental model that includes patch‐specific optimal controls, such as treated mosquito nets, insecticide spraying, and antimalaria drugs. We first established that the model solutions remain bounded and nonnegative, thereby confirming the mathematical and epidemiological validity of the model. Using the next‐generation matrix technique, we computed the basic reproduction number, . It is critically dependent on both temperature variability and human movement. Stability analysis indicates that the malaria‐free equilibrium point is both locally and globally asymptotically stable when and becomes unstable if it exceeds one. Actual prevalence data for malaria in Ilu Ababor and Gambella, Ethiopia, from 2018 to 2025 were used to validate the model. To assess the effects of patch‐specific interventions, simulations were conducted within an optimal control framework. The results demonstrate that the simultaneous application of all three management strategies effectively reduces the spread of malaria in both patches. The main novelty is the integration of optimal controls across two patches, along with real‐data validation and combined patch‐specific controls, providing a more realistic and policy‐relevant framework than traditional malaria models that focus on a single homogeneous population.